Feng Yunpeng, Cheng Haobo, Zhang Shaohua
Appl Opt. 2023 Sep 20;62(27):7288-7298. doi: 10.1364/AO.497402.
In modern ultra-precision polishing, sub-aperture technologies are prone to mid-spatial frequency errors due to identical patterns of a path. A random tool path on a regular point set is widely used to suppress mid-spatial frequency errors. In this study, two non-grid uniform point sets, the Fibonacci and the three-directional, were introduced into optical polishing. To solve the time-consuming problem caused by a large amount of distance calculation, a distance-based weighted random (DBWR) algorithm and a linear programming and connecting (LPC) algorithm were presented. The DBWR algorithm reduces the generation time by strengthening the weight of the neighboring points in a specific direction, while the LPC algorithm adjusts the order and distance of points artificially. Then a random stitching method was proposed for the large-scale point set applying to large-sized optical surfaces, which dramatically reduced the generation time. Finally, experiments validated that the algorithms for non-grid sets can be effectively used for optical surface figuring without introducing an apparent mid-spatial frequency.
在现代超精密抛光中，由于路径模式相同，子孔径技术容易产生中空间频率误差。规则点集上的随机刀具路径被广泛用于抑制中空间频率误差。在本研究中，将两种非网格均匀点集，即斐波那契点集和三向点集，引入到光学抛光中。为了解决大量距离计算导致的耗时问题，提出了基于距离的加权随机（DBWR）算法和线性规划与连接（LPC）算法。DBWR算法通过增强特定方向上相邻点的权重来减少生成时间，而LPC算法则人工调整点的顺序和距离。然后针对适用于大型光学表面的大规模点集提出了一种随机拼接方法，该方法显著减少了生成时间。最后，实验验证了非网格集算法可有效用于光学表面整形，且不会引入明显的中空间频率。
